Because of the dynamic range of the signals which must be accurately displayed in analytical spectrometers, large computer memories of 20 bits per channel are not uncommon. In ensemble averaging computers, a process of scaling the data in the memory channels and the incoming data has been utilized in that it permits the use of smaller memory channels. By this process, whenever it became apparent that further accumulation would produce overflow in the memory channel, the data in the channel is scaled, for example, divided by two, and the input data from subsequent scans is also divided by two before being added to memory. This scaling process permits continued accumulation with a memory having a lesser number of bits but it implies that the lower value bits from the analogue to digital converter are not being accumulated. Prior art spectrometers which employ scaling operations, did not recognize that unlimited accumulation of data did not necessarily improve the signal-to-noise ratio. In fact, under certain conditions, continued accumulation leads to a deterioration in the signal-to-noise ratio.